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Publisher: Cambridge University Press   (Total: 367 journals)

 Compositio Mathematica   Journal Prestige (SJR): 2.965   Citation Impact (citeScore): 37   Number of Followers: 1          Subscription journal    ISSN (Print) 0010-437X - ISSN (Online) 1570-5846    Published by Cambridge University Press  [367 journals]
• On Følner sets in topological groups
• Authors: Friedrich Martin Schneider; Andreas Thom
Pages: 1333 - 1361
Abstract: We extend Følner’s amenability criterion to the realm of general topological groups. Building on this, we show that a topological group $G$ is amenable if and only if its left-translation action can be approximated in a uniform manner by amenable actions on the set  $G$ . As applications we obtain a topological version of Whyte’s geometric solution to the von Neumann problem and give an affirmative answer to a question posed by Rosendal.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X1800708X
Issue No: Vol. 154, No. 7 (2018)

• Derived categories of Gushel–Mukai varieties
• Authors: Alexander Kuznetsov; Alexander Perry
Pages: 1362 - 1406
Abstract: We study the derived categories of coherent sheaves on Gushel–Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety is even or odd. We analyze the basic properties of this category using Hochschild homology, Hochschild cohomology, and the Grothendieck group. We study the K3 category of a Gushel–Mukai fourfold in more detail. Namely, we show this category is equivalent to the derived category of a K3 surface for a certain codimension 1 family of rational Gushel–Mukai fourfolds, and to the K3 category of a birational cubic fourfold for a certain codimension 3 family. The first of these results verifies a special case of a duality conjecture which we formulate. We discuss our results in the context of the rationality problem for Gushel–Mukai varieties, which was one of the main motivations for this work.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007091
Issue No: Vol. 154, No. 7 (2018)

• Arithmetic intersection on GSpin Rapoport–Zink spaces
• Authors: Chao Li; Yihang Zhu
Pages: 1407 - 1440
Abstract: We prove an explicit formula for the arithmetic intersection number of diagonal cycles on GSpin Rapoport–Zink spaces in the minuscule case. This is a local problem arising from the arithmetic Gan–Gross–Prasad conjecture for orthogonal Shimura varieties. Our formula can be viewed as an orthogonal counterpart of the arithmetic–geometric side of the arithmetic fundamental lemma proved by Rapoport–Terstiege–Zhang in the minuscule case.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007108
Issue No: Vol. 154, No. 7 (2018)

• ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$(\mathbb{P}^{1})^{n}$ ++++++++++++ ++++++++ ++++ +++++++++++++++&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2018&rft.volume=154&rft.spage=1441&rft.epage=1472&rft.aulast=Ghioca&rft.aufirst=Dragos&rft.au=Dragos+Ghioca&rft.au=Khoa+D.+Nguyen,+Hexi+Ye&rft_id=info:doi/10.1112/S0010437X18007157">The dynamical Manin–Mumford conjecture and the dynamical Bogomolov
conjecture for endomorphisms of  $(\mathbb{P}^{1})^{n}$
• Authors: Dragos Ghioca; Khoa D. Nguyen, Hexi Ye
Pages: 1441 - 1472
Abstract: We prove Zhang’s dynamical Manin–Mumford conjecture and dynamical Bogomolov conjecture for dominant endomorphisms $\unicode[STIX]{x1D6F7}$ of $(\mathbb{P}^{1})^{n}$ . We use the equidistribution theorem for points of small height with respect to an algebraic dynamical system, combined with an analysis of the symmetries of the Julia set for a rational function.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007157
Issue No: Vol. 154, No. 7 (2018)

• ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\ell$ ++++++++++++ ++++++++ ++++ +++++++++++++++-blocs+de+niveau+zéro+des+groupes+ ++++++++++++++++++ ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$p$ ++++++++++++ ++++++++ ++++ +++++++++++++++-adiques&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2018&rft.volume=154&rft.spage=1473&rft.epage=1507&rft.aulast=Lanard&rft.aufirst=Thomas&rft.au=Thomas+Lanard&rft_id=info:doi/10.1112/S0010437X18007133">Sur les $\ell$ -blocs de niveau zéro des groupes $p$ -adiques
• Authors: Thomas Lanard
Pages: 1473 - 1507
Abstract: Let $G$ be a $p$ -adic group that splits over an unramified extension. We decompose $\text{Rep}_{\unicode[STIX]{x1D6EC}}^{0}(G)$ , the abelian category of smooth level $0$ representations of $G$ with coefficients in $\unicode[STIX]{x1D6EC}=\overline{\mathbb{Q}}_{\ell }$ or $\overline{\mathbb{Z}}_{\ell }$ , into a product of subcategories indexed by inertial Langlands parameters. We construct these categories via systems of idempotents on the Bruhat–Tits building and Deligne–Lusztig theory. Then, we prove compatibilities with parabolic induction and restriction functors and the local Langlands correspondence.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007133
Issue No: Vol. 154, No. 7 (2018)

• Cremona transformations and derived equivalences of K3 surfaces
• Authors: Brendan Hassett; Kuan-Wen Lai
Pages: 1508 - 1533
Abstract: We exhibit a Cremona transformation of $\mathbb{P}^{4}$ such that the base loci of the map and its inverse are birational to K3 surfaces. The two K3 surfaces are derived equivalent but not isomorphic to each other. As an application, we show that the difference of the two K3 surfaces annihilates the class of the affine line in the Grothendieck ring of varieties.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007145
Issue No: Vol. 154, No. 7 (2018)

• Rank 3 rigid representations of projective fundamental groups
• Authors: Adrian Langer; Carlos Simpson
Pages: 1534 - 1570
Abstract: Let $X$ be a smooth complex projective variety with basepoint $x$ . We prove that every rigid integral irreducible representation $\unicode[STIX]{x1D70B}_{1}(X\!,x)\rightarrow \operatorname{SL}(3,\mathbb{C})$ is of geometric origin, i.e., it comes from some family of smooth projective varieties. This partially generalizes an earlier result by Corlette and the second author in the rank 2 case and answers one of their questions.
PubDate: 2018-07-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007182
Issue No: Vol. 154, No. 7 (2018)

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